↑

Properties

Label 1232.4.z
Level $1232$
Weight $4$
Character orbit 1232.z
Rep. character $\chi_{1232}(113,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $432$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1232.z (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1232, [\chi])\).

Total New Old
Modular forms 2352 432 1920
Cusp forms 2256 432 1824
Eisenstein series 96 0 96

Trace form

\( 432 q - 14 q^{7} - 1012 q^{9} + O(q^{10}) \) \( 432 q - 14 q^{7} - 1012 q^{9} + 10 q^{11} - 12 q^{15} + 152 q^{17} + 164 q^{23} - 2700 q^{25} - 444 q^{27} + 200 q^{29} - 956 q^{33} + 420 q^{35} - 12 q^{37} - 1452 q^{39} + 40 q^{41} - 2524 q^{43} - 2280 q^{47} - 5292 q^{49} + 1692 q^{51} + 564 q^{53} + 1080 q^{55} - 2012 q^{57} - 120 q^{59} - 630 q^{63} - 876 q^{67} - 2862 q^{71} - 1656 q^{73} - 5484 q^{75} - 476 q^{77} - 2690 q^{79} - 8048 q^{81} + 4020 q^{83} + 1944 q^{85} - 2736 q^{87} + 4600 q^{89} + 1368 q^{93} - 1180 q^{95} - 596 q^{97} - 6340 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)